Question

Margetis Inc. carries an average inventory of $750,000. Its annual sales are $10 million, its cost of goods sold is 75% of annual sales, and its average collectionperiod is twice as long as its inventory conversion period. The firm buys on terms of net 30 days, and it pays on time. Its new CFO wants to decrease the cashconversion cycle by 10 days, based on a 365-day year. He believes he can reduce the average inventory to $647,260 with no effect on sales. By how much must the firmalso reduce its accounts receivable to meet its goal in the reduction of the cash conversion cycle?

Answer 1

Annual sales	$10,000,000
Cost of goods sold	$7,500,000
Cost of goods sold	= opening stock+purchase- Closing stock
Purchases	= $7500000
Accounts payable	= 30 days
Inventory conversion period	= Average inventory / Cost of goods sold per day
Cost of goods sold per day	= 7500000 / 365
	= $20,548
Inventory convertion period	= 750000/20548
	= 36.5 days
Average collection periode	= 36.5 * 2
	= 73 days
Cash Conversion Cycle	= 73 + 36.5 - 30
	= 79.5 days
As per given amount:
Inventory convertion period	= 647260/20548
	= 31.5 days
Average collection periode	= 63 days
Cash conversion cycle	= +63+31.5-30
	= 64.5 days
Decrease to 10 day's means:
Cash Conversion Cycle	= 69.5 days
Accounts receivable+inventory-accounts payable	= 69.5
Accounts receivable + inventory -30	= 69.5
x^2+x-30	= 69.5
x^2+x	= 69.5+30
3x	= 99.5
x	= 99.5/3
	= 33.17 days
Inventory convertion period	= 33.17
Average collection period	= 66.34
Accounts receivable	= 33.17*20548
	= $681,577
Verification:
Inventory conversion period	= 681577/20548
	= 33.17 days
Average collection periode	= 33.17*2
	= 66.34 days
Accounts payable	= 30 days
Cash conversion cycle	= 66.34+33.17-30
	= 69.5 days

Thank you....